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Example 2.3: The earth subtends an angle of 17:3 when viewed fromgeostationary orbit. Estimate the dimensions and gain of pyramidal hornand conical horn antennas, which will provide global coverage at 4.5 GHz.SolutionBy assuming a uniformly illuminated wave across the aperture (lengthand breadth) of the pyramidal antenna, we can take the beamwidths in the E-and H-planes to be the same, that is,y ¼ 17:3 ¼ y E ¼ y H :Take the antenna’s efficiency Z ¼ 50%. Then the wavelength l ¼ c=f ¼0:3 10 9 =4:5 10 9 ¼ 6:67 cm.From (2.39) and (2.40), we can compute the aperture dimensions:A ¼ 30:06 cmB ¼ 20:81 cmGain G ¼ 19:46 dBSimilarly, the dimensions and gain of the conical can be computed using(2.42) and (2.43):aperture diameter D ¼ 22:35 cm and gain G ¼ 17:63 dB2.7.2 Re£ector=Lens Antenna SystemThe most straightforward design of reflector or lens antennas uses parabolicgeometry. The reflector antenna, one of the two most popular for earth stationantennas, consists of a reflector—a section of a surface formed by rotating aparabola about its axis—and a feed whose phase is located at the focal point ofthe paraboloid reflector. This is the main reason the reflector antenna is alsocalled the prime focus antenna. The size of the antennas is represented by thediameter D of the reflector; see Fig. 2.13. For any value of a, the geometricproperty of the parabola dictates thatfa þ ab ¼ constantð2:44ÞThe paraboloid reflector is capable of focusing at infinity the electromagneticrays coming out of its focus. From spherical geometry it is easily recognizedthat when a primary point-source reflector (also called the feed) generatesspherical wavefronts, they are converted to plane-wave fronts at the antennaaperture. This is consistent with geometric optic approximation, namely, rayCopyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.